The Axiomatic Characterization of the Value in Cooperative Game Theory

The Shapley value, one of the most widespread concepts in operations Research applications of cooperative game theory, was defined and axiomatically characterized in different game-theoretic models. In this paper we provide a new axiomatization of the Shapley value which probably is the most important one-point solution concept for the cooperative games using a differential marginality axiom. This axiom states that two players’ payoff differential is completely determined by the differences of their marginal contributions. Efficiency means that the worth generated by the grand coalition is fully allocated to the players. Null player property means that the marginal contributions of null players in a game are zero payoffs. In this study we show that the Shapley value is redefined by efficiency axiom, the null player property and differential marginality axiom.